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The hot spots conjecture is only known to be true for special geometries. This paper shows numerically that the hot spots conjecture can fail to be true for easy to construct bounded domains with one hole. The underlying eigenvalue problem for the Laplace equation with Neumann boundary condition is solved with boundary integral equations yielding a non-linear eigenvalue problem. Its discretization via the boundary element collocation method in combination with the algorithm by Beyn yields highly accurate results both for the first non-zero eigenvalue and its corresponding eigenfunction which is due to superconvergence. Additionally, it can be shown numerically that the ratio between the maximal/minimal value inside the domain and its maximal/minimal value on the boundary can be larger than 1 + 10− 3. Finally, numerical examples for easy to construct domains with up to five holes are provided which fail the hot spots conjecture as well.
The proposed Den Haag Zuidwest district heating system of the city of The Hague consists of a deep doublet in a Jurassic sandstone layer that is designed for a production temperature of 75 °C and a reinjection temperature of 40 °C at a flow rate of 150 m3 h−1. The prediction of reservoir temperature and production behavior is crucial for success of the proposed geothermal doublet. This work presents the results of a study of the important geothermal and geohydrological issues for the doublet design. In the first phase of the study, the influences of the three-dimensional (3D) structures of anticlines and synclines on the temperature field were examined. A comprehensive petrophysical investigation was performed to build a large scale 3D-model of the reservoir. Several bottomhole temperatures (BHTs), as well as petrophysical logs were used to calibrate the model using thermal conductivity measurements on 50 samples from boreholes in different lithological units in the study area. Profiles and cross sections extracted from the calculated temperature field were used to study the temperature in the surrounding areas of the planned doublet. In the second phase of the project, a detailed 3D numerical reservoir model was set up, with the aim of predicting the evolution of the producer and injector temperatures, and the extent of the cooled area around the injector. The temperature model from the first phase provided the boundary conditions for the reservoir model. Hydraulic parameters for the target horizons, such as porosity and permeability, were taken from data available from the nearby exploration wells. The simulation results are encouraging as no significant thermal breakthrough is predicted. For the originally planned location of the producer, the extracted water temperature is predicted to be around 79 °C, with an almost negligible cooling in the first 50 years of production. When the producer is located shallower parts of the reservoir, the yield water temperatures is lower, starting at ≈76 °C and decreasing to ≈74 °C after 50 years of operation. This comparatively larger decrease in temperature with time is caused by the structural feature of the reservoir, namely a higher dip causes the cooler water to easily move downward. In view of the poor reservoir data, the reservoir simulation model is constructed to allow iterative updates using data assimilation during planned drilling, testing, and production phases. Measurements during an 8 h pumping test carried out in late 2010 suggest that a flow rate of 150 m3 h−1 is achievable. Fluid temperatures of 76.5 °C were measured, which is very close to the predicted value.
The entangled Universe
(2004)
Humic substances originating from various organic matters can ameliorate soil properties, stimulate plant growth, and improve nutrient uptake. Due to the low calorific heating value, leonardite is rather unsuitable as fuel. However, it may serve as a potential source of humic substances. This study was aimed at characterizing the leonardite-based soil amendments and examining the effect of their application on the soil microbial community, as well as on potato growth and tuber yield. A high yield (71.1%) of humic acid (LHA) from leonardite has been demonstrated. Parental leonardite (PL) and LHA were applied to soil prior to potato cultivation. The 16S rRNA sequencing of soil samples revealed distinct relationships between microbial community composition and the application of leonardite-based soil amendments. Potato tubers were planted in pots in greenhouse conditions. The tubers were harvested at the mature stage for the determination of growth and yield parameters. The results demonstrated that the LHA treatments had a significant effect on increasing potato growth (54.9%) and tuber yield (66.4%) when compared to the control. The findings highlight the importance of amending leonardite-based humic products for maintaining the biogeochemical stability of soils, for keeping their healthy microbial community structure, and for increasing the agronomic productivity of potato plants.